Vertical translations occur outside the absolute value, while horizontal translations occur inside the absolute value.
Practice makes perfect
We are asked to graph the given function by translating the parent function y=|x|. When translating absolute value functions, verticaltranslations occur after the absolute value has been evaluated. This is why they are outside the absolute value symbols. Consider the following general equation, where k is a real number.
y=|x|+ k
The graph of this equation is a vertical translation of y=|x| by k units. Let's start with the graph of y=|x|.
Now let's look at the given function again.
y=|x|-2 ⇒ y=|x|+( -2)
In this case, k is equal to - 2. Since this value is negative, the transformation will move the graph of y=|x| down by 2. As an example, we will translate three points on the line y=|x| down by 2 units.
Translating each and every point 2 units down means shifting the entire graph of y=|x| down by 2 units.
